2,161 research outputs found
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)
We consider a tensor product V(b)= \otimes_{i=1}^n\C^N(b_i) of the Yangian
evaluation vector representations. We consider the action of the
commutative Bethe subalgebra on a -weight subspace
of weight . Here the Bethe algebra depends
on the parameters . We identify the -module
with the regular representation of the algebra of functions on a
fiber of a suitable discrete Wronski map. If , we study the action
of on a space of singular vectors of a certain
weight. Again, we identify the -module with the
regular representation of the algebra of functions on a fiber of another
suitable discrete Wronski map.
These results we announced earlier in relation with a description of the
quantum equivariant cohomology of the cotangent bundle of a partial flag
variety and a description of commutative subalgebras of the group algebra of a
symmetric group.Comment: Latex, 23 pages, misprints correcte
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